Engineered antibodies are a large and growing class of protein therapeutics comprising both marketed products and many molecules in clinical trials in various disease indications. We investigated naturally conserved networks of amino acids that support antibody V(H) and V(L) function, with the goal of generating information to assist in the engineering of robust antibody or antibody-like therapeutics. We generated a large and diverse sequence alignment of V-class Ig-folds, of which V(H) and V(L) domains are family members. To identify conserved amino acid networks, covariations between residues at all possible position pairs were quantified as correlation coefficients (phi-values). We provide rosters of the key conserved amino acid pairs in antibody V(H) and V(L) domains, for reference and use by the antibody research community. The majority of the most strongly conserved amino acid pairs in V(H) and V(L) are at or adjacent to the V(H)-V(L) interface suggesting that the ability to heterodimerize is a constraining feature of antibody evolution. For the V(H) domain, but not the V(L) domain, residue pairs at the variable-constant domain interface (V(H)-C(H)1 interface) are also strongly conserved. The same network of conserved V(H) positions involved in interactions with both the V(L) and C(H)1 domains is found in camelid V(HH) domains, which have evolved to lack interactions with V(L) and C(H)1 domains in their mature structures; however, the amino acids at these positions are different, reflecting their different function. Overall, the data describe naturally occurring amino acid networks in antibody Fv regions that can be referenced when designing antibodies or antibody-like fragments with the goal of improving their biophysical properties.